Mergers of BBH systems which have spins that are isotropic in orientation, as is expected from dynamical formation scenarios, implies a distribution of \(\chi _{\rm eff}\)  symmetric about 0 (see the black line in Figure REF ). This prediction comes from the idea that during a dynamical capture, there is no reason to expect that the two BHs should have correlated spin directions when they randomly encounter each other. In contrast, spins of BBH systems forming from common evolution are expected to remain primarily aligned with the orbital angular momentum, resulting in exclusively positive values for \(\chi _{\rm eff}\)  from this population. While the distribution of \(\chi _{\rm eff}\)  we recover appears symmetric, it is centered at \(\chi _{\rm eff} = {0.033}^{+0.034}_{-0.038}\) , favoring a positive central location but consistent with being centered at \(\chi _{\rm eff} = 0\)  at the 90% level. This result, coupled with the result that \({38.7\%}^{+12.8\%}_{-11.5\%}\)  of events have \(\chi _{\rm eff} < 0\) , presents the possibility that dynamical encounters are a significant contribution to the formation mechanisms of BBH merger systems. This is in contrast to the results reported in [1]} that the \(\chi _{\rm eff}\)  distribution is centered at 0.06 and rules out being centered at 0 at the 90% level; this result is obtained by modeling the \(\chi _{\rm eff}\)  distribution as a Gaussian with the mean and standard deviation as free parameters [2]}, [1]}. While we use a largely identical event list in our analyses, the modeling assumptions for the \(\chi _{\rm eff}\)  distribution made in [1]} probably explain some of the differences in our results. While [5]}, [6]} also find a \(\chi _{\rm eff}\)  distribution consistent with being centered at zero, [5]} does not find any support for \(\chi _{\rm eff} < 0\) ; such a difference may also be due to different modeling choices for the population of \(\chi _{\rm eff}\) .
